Problem: Which of these numbers is prime? ${9,\ 31,\ 45,\ 69,\ 82}$
A prime number has exactly two factors: 1 and itself. The factors of 9 are 1, 3, and 9. The factors of 31 are 1 and 31. The factors of 45 are 1, 3, 5, 9, 15, and 45. The factors of 69 are 1, 3, 23, and 69. The factors of 82 are 1, 2, 41, and 82. Thus, 31 is a prime number.